Buchstaber, VM and Mikhailov, AV (2017) Infinite-dimensional Lie algebras determined by the space of symmetric squares of hyperelliptic curves. Functional Analysis and Its Applications, 51 (1). pp. 2-21. ISSN 0016-2663
Abstract
We construct Lie algebras of vector fields on universal bundles of symmetric squares of hyperelliptic curves of genus g = 1, 2,.. For each of these Lie algebras, the Lie subalgebra of vertical fields has commuting generators, while the generators of the Lie subalgebra of projectable fields determines the canonical representation of the Lie subalgebra with generators L₂q, q = −1, 0, 1, 2,.., of the Witt algebra. As an application, we obtain integrable polynomial dynamical systems.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2017, Springer Science+Business Media New York. This is an author produced version of a paper published in Functional Analysis and Its Applications. Uploaded in accordance with the publisher's self-archiving policy. The final publication is available at Springer via https://doi.org/10.1007/s10688-017-0164-5 |
Keywords: | infinite-dimensional Lie algebras; representations of the Witt algebra; symmetric polynomials; symmetric powers of curves; commuting operators; polynomial dynamical systems |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Funding Information: | Funder Grant number Royal Society 2014/R3 |
Depositing User: | Symplectic Publications |
Date Deposited: | 14 Nov 2017 11:32 |
Last Modified: | 31 Jan 2019 15:22 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s10688-017-0164-5 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:123925 |